Calculate $\sqrt{\sqrt[3]{0.000064}}$. Express your answer as a decimal to the nearest tenth.
We start by writing the decimal as a fraction, and we find \begin{align*}
\sqrt{\sqrt[3]{0.000064}} &= \sqrt{\sqrt[3]{\frac{64}{10^6}}} = \sqrt{\left(\frac{2^6}{10^6}\right)^{\frac13}}\\
&=\sqrt{\frac{2^{6\cdot \frac{1}{3}}}{10^{6\cdot \frac13}}} = \sqrt{\frac{2^2}{10^2}} = \frac{2}{10} = \boxed{0.2}.
\end{align*}